Since times immemorial mankind was fortunatelly equipped with sense for time, and many ancient cultures occupied themselves with creating calendar on one or another type. From those we still remember there are Aztecs and Mayan , Egyptians, Druids, different tribes belonging to American Indian heritage, on the other side of the globe there were Chinese ,
Jews , Indian etc. I'm not going too deep now to draw historical links between these yet known to us cultures to show how they were interconnected and where from each of their particular astrological /astronomical systems derived, enough to say that the knowledge was passed without major breaks from one culture to another, survived rise and falls of many civilisations.
Not to forget there were countless such before we know almost nothing about.

Our ancestors used almost the same type of hypothetical reasoning as modern astrophysicists while they've predicted inter-planetary and inter-galctic influences on our little planet.
Indeed they did not think that Stars are little lamps shining on sky , they knew they are other Suns, other worlds with their own living categories.

Yet, not one of the astrological systems is exactly the same as the other, though you can observe many natural similarities depending more on accuracy of their calculation.

The differences , countless and various are very similar to multitude of variety of hypothesis in modern physics.
Some systems were geocentric, other heliocentric, some counted more celestial bodies to the equation, others less.

The one more common feature to all was an effort to draw closed time cycle model, we vaguely call calendar or zodiac , to simplify all the complication to something human mind is able to contain .
Closed systems is something human mind can rely on when facing all the infinity of life and universe,
calendar with beginning and end, head and foot so to say.
Unstructured infinity is not more than organized chaos, too difficult to work with.

Few years back i was quite fascinated when reading a book about Mayans, and the subtle interractions they saw happening between different solar systems, the baktuns, cycles of time when our Sun and planet are under dominant influence of another particular Star etc.
There's still lots we do not know about relations between star systems in universe but with time and evolution of physics, i'm sure these will be explored .

Straight to the point. If our calendar 'predicts' that 31st December is the end of they year, or better to say, if on 21st of March Sun enters 'to the sign of Aries' ( poetic expression in a sense ) , does it mean that something big will happen on the next day ?

Well, some believe it, or at least they did in a past.

Calendar however long is not more than closed system , because basically no one can draw end-less calendar. If Mayans survived their time they'd continue with describing the cycles further on, i believe.

There is something positive on rising the global awareness, becoming aware of large cycles of time . It's important for people to collect their minds and feel protective about their our kind.